3.3 Stabilization of the monolayer and sample quality
3.3.4 Flatness of the interface
After a sample is placed into the experimental setup, it usually takes several weeks of treatment before the sample can be considered as equilibrated and at. The treatment strategies and stabilization problems of the sample proles are discussed now.
When the binary suspension is lled into the glass sample cell using a conventional1ml syringe, the particles sediment to the water-air interface on the timescale of minutes.
Usually at the beginning of sample treatment, the density proles across the sam-ple cell (x- and y-direction) are very inhomogeneous as shown in the upper graphs of Figure 3.12. The upper group of curves represents only the big particles and the lower group the small particles. Both groups of scans do not scale as expected for a mixture with homogeneous relative concentration: particle species segregate at the beginning,
46This value is calculated from the geometry of the tripod and the maximum corrections of the actuator positions.
Figure 3.12: Top: Scans of particle numbers NA and NB per eld of view are shown, scanned in x- and y-direction few hours after the sample was lled in the sample cell.
Bottom: Scans after several weeks of equilibration and treatment.
Scans are shown in all graphs separately for big (A) and small (B) species as indicated.
The groups of curves consist each of ten scans with two hours waiting time after every scan starting with a black curve and ending with an orange one. Not the whole cross section over the sample cell is shown because the illumination in the missing part was weaker due to reections from the inside bore of the copper block. No prole infor-mation was obtainable in this area using light source No. I (see section 3.2.1). This particular sample had a considerable drift causing the uctuations in the scans of the small particles in the bottom graphs.
Figure 3.13: Scans of particle numbers NA and NB per eld of view are shown sepa-rately, scanned in x- and y-direction after several weeks of sample treatment and equili-bration. The density of the big particles is homogeneous in both directions. The density prole of the small particles is only at in the y-direction. The three groups of curves in both graphs consist each of ten scans with two hours waiting time after every scan starting with a black curve and ending with an orange one (they overlap as proles are almost identical). Not the whole cross section over the sample cell is shown because the illumination in the missing part was weaker due to reections from the inside bore of the copper block. No information on the particle species was obtainable in this area using light source No. I from below (see section 3.2.1). The interaction parameter was Γ = 559. No temporal change in both density proles is found, and the sample had no drift.
and the local relative concentration of small particles is then higher at the cells edge if the interface is convex (this phenomenon will be discussed in section 3.3.6). Every two hours a prole scan is performed to track the development of the sample proles.
The scans show that the sample is denser in the center due to a convex interface, not stable over time, not symmetric and heterogenous in relative concentration.
To equilibrate the density and atten the interface, the density control (see section 3.3.2) is used to correct the number of big particles towards lower values over many days or weeks. With the tilt control the inclination of the setup is adjusted to reach a horizontal interface and therefore symmetric density proles. Only 200µrad per day and per axis are corrected for this is the timescale of prole equilibration47. The lower graphs of Figure 3.12 show xy-scans of the same sample several weeks later.
47Here, 'equilibration' does not mean that the density prole is at. It only means that the proles are stable over time. Density proles equilibrate faster for low values of Γ, but regulation is more stable for high interaction strengthsΓ.
Both proles are at and stable over time. In this example the variation of the density is ±3% and ±8% for the big and the small particles respectively. The uctuations of the small particles can be explained by a drift in the particle plane in this particular sample. The local distribution of the small particles is naturally less homogenous com-pared to the big particles ('partial clustering', see section 5.1), and therefore a drift causes these uctuations when the small beads drift over the edge of the eld of view.
The atness of the small particle prole was not always reached as shown in this ex-ample. As shown in Figure 3.13, spacial variations of several hundred small particles have been observed across the cell diameter while the density of big particles is homo-geneous. Furthermore, the particle density regulation is controlling the local density of big particles and only indirectly the density of the small ones. Two additional eects make it dicult to achieve a homogeneous distribution of small particles: segregation in a gravitational eld and heterogeneous adsorption of particle species at the edge of the cell. These eects will be discussed in the sections 3.3.6 and 3.3.7 respectively.
Since the big particles are much more sensitive to tilt and curvature of the interface, and the prole of the small particles cannot be controlled directly (see section 3.3.5), the prole of the big particles was chosen as criteria for sucient atness of the sample.
For data acquisition a position in the sample is chosen where the distribution of small particles is homogenous over the eld of view.